Using examples from the literature, I try to show how astrophysical parameters of pulsating stars are derived and how certain (or, occasionally, uncertain) they are. The examples are arranged in the order of increasing input of a priori knowledge. Thus, I start with pulsation periods, because in most cases they can be obtained directly from observations. Then I consider the two stars for which pulsation constants have been determined without recourse to photometric calibrations. Next I show how multicolour photometry can help identify pulsation modes. Finally, I discuss the photometric Teff, log g, and pulsation constants. This leads to conclusions which contain some recommendations for the observers, including a list of promising targets for asteroseismology.

Results of the recent stability surveys (Dziembowski and Pamyatnykh 1993; Gautschy and Saio 1993) leave no doubts that the opacity mechanism is responsible for oscillations observed in β Cephei stars. The linear nonadiabatic analysis used to determine the instability domains in the HR diagram, yields also quantities that may be compared with observations. These nonadiabatic observables are evaluated from the complex eigenfunctions y(r) and f(r) describing variations of the radial displacement and the bolometric flux, respectively. Both y and f are very nearly constant within the stellar atmosphere. The eigenfunctions describing the horizontal displacement and variations of thermodynamical quantities may be expressed in terms of y and f. Since the linear eigenfunctions may be arbitrarily normalized, there are only two real independent observables. We may choose them to be and ψ = arg(f/y). Using static atmosphere models, with the inertial term included in the effective gravity, we may evaluate amplitude ratios and phase differences for integrated changes in directly measured parameters (Dziembowski 1977, Stamford and Watson 1981, Watson 1988).

As first pointed out by Moskalik and Dziembowski (1992) all β Cephei stars lie within the domain of H–R diagram where κ-mechanism effectively drives pulsations in the stellar layers with T ≈ 2×105 K. For most of these objects a chemical composition described by X = 0.70 and Z = 0.02 is sufficient to account for the pulsations, cf. Dziembowski and Pamyatnykh (1993). Recently, Cugier, Dziembowski and Pamyatnykh (1993) have investigated how the present knowledge about nonadiabatic observables of β Cephei stars affects methods of identification of the spherical harmonic degree, l. They found that good photometric and radial velocity data should result in unambiguous identification of l. Cugier, Dziembowski and Pamyatnykh also concluded that nonadiabatic observables can be used to obtain mean stellar parameters of pulsating stars.

BW Vulpeculae is a large amplitude β Cephei-type star, pulsating with a single period of 0.20104 day. Its nonlinear modeling was first attempted by Pesnell & Cox (1980). Because the true instability mechanism was not known then, the pulsation amplitude was imposed in that study in an arbitrary fashion.

The results of the study of period changes of all pulsational components in the multiperiodic β Cephei-type star, 12 Lac, are summarized.

α Lup (HR 5469) is a multiperiodic beta Cep star. According to Shobbrook (1979) and Lampers & Goossens (1982) the main period (P=0.25985 day) corresponding to the radial mode is constant. The amplitude of the secondary period, attributed to a non radial mode, is so small that it does not affect the determination of maximum dates.

β Cru (HR 4853) is a multiperiodic β Cep star. The main period has been found constant between 1958 and 1973 by Cuypers (1982). In order to extend the basis of the ephemeris, we computed two values of radial velocity maxima from individual measurements published by Campbell & Moore (1928) and Sahade & Albarracin (1952). In lack of simultaneous spectroscopic and photometric observations, we used an arbitrary value equal to 0.25 period for the phase lag.

We give a progress report on an observational program intended to determine detailed chemical abundances of β Cephei stars and constant stars with similar temperature and gravity. There is some evidence that non-variable stars have a lower metal content than variables, as the recently found pulsation mechanism would suggest.

The β Cephei instability is believed to be caused by the κ-mechanism. Model calculations, based on revised metal opacities, show this mechanism to be strongly sensitive to metallicity (e.g., Dziembowski, W. A. & Pamyatnykh, A. A., 1993: MNRAS, 262, 204). It appears that [Fe/H] must be larger than the solar value in order to drive the β Cephei pulsations. For this reason, the models predict that no β Cephei stars should be found in the Magellanic Clouds. Balona (1992: MNRAS, 256, 425; 1992: ASP Conf. Ser., Vol. 30, 155; 1993: MNRAS, 260, 795) has tested this prediction by observing three young clusters in the SMC and LMC (NGC 330, NGC 2004 and NGC 2100). He found no β Cephei stars down to a magnitude of V ≈ 16; the threshold for detection of variability on time-scales of a few hours was 10 mmag. Most Galactic β Cephei stars have amplitudes greater than this, but we might expect β Cephei stars in the Magellanic Clouds (if they exist) to have smaller amplitudes, due to the different environment. To test this, we have observed two young clusters NGC 371 (SMC) and NGC 2122 (LMC) with high sensitivity.

Known as well as β CMa stars, the classical β Cep stars are a group of variables of spectral type between BO to B2 and luminosity classes II to IV with light and radial velocity periods between 3 and 7 hours and radial velocity ranges usually < 50 km/sec. Their photometric amplitudes are usually < 0.1 mag in the visible. The light curves are approximately sinusoidal (however, multiple modes are frequently detected with low amplitudes), which lag about 90° behind the radial velocity curve and the color changes in the blue and visual spectral regions are small. Color and luminosity show that maximum temperature coincides with minimum radius. Probably not all the stars in this spectral range are variables; most investigators searching in this region for β Cep variables have observed that a large number of stars in this zone are constant in light. Also, the β Cep stars are not different spectroscopically from nonvariable stars of the same MK type.

The B type star 53 Persei was discovered in 1977 by Smith (1977) as the prototype of a separate group of B-type variables showing light and line profile variability. The physical cause of the variability was thought to be nonradial pulsation (NRP) (see, e.g. Smith et al. 1984). However, the NRP model for this star has been questioned by Balona (1986) who suggested the rotational modulation (RM) model to explain the variability. In order to resolve the long lasting debate about 53 Persei, a campaign was initiated to organize coordinated optical photometry and spectroscopy from the ground, and Far-UV photometry from Voyager in 1991 January. This paper presents the results of period analysis on the groundbased UBV data. In another paper, Smith & Huang (1994) report the new identification of pulsation modes using Voyager Far-UV photometry combined with the results from optical observations. Some preliminary results from APT uvby observations taken at a single site are also cited for comparison.

Huang et al. (1994) have conducted an extensive photometric campaign on the prototypical nonradially pulsating (NRP) star 53 Per and confirmed the pair of frequencies at 0.46 cy d-1 (dominant) and 0.60 cy d-1 originally reported by BS79. In an analysis of these two modes, SP79 underestimated the effects of the Balmer jump on this star's color variation, leading them to an erroneous conclusion that geometric effects dominate the color variations and also that the modes are described by indices l=3, -m = 3 and 2. Herein we describe results from Voyager 2 observations obtained during Lin's optical campaign. The amplitudes derived for these Far-UV data using the optical ephemeris provide for the first time a large enough wavelength baseline to discriminate in favor of thermal effects over geometrical ones in producing NRP light variations. In addition, they allow the dominant mode to be constrained to l = 2 (or 1).

ζ Cas (HR 153, mv=3.66, vsini=18 kms-1) was classified as a 53 Per variable by Smith (1980). He detected variations in the profile of the 4552 Å Si III line with a period of 0.9 day. The radial velocity and the luminosity were observed to be constant by Abt & Levy (1978) and by Jerzykiewicz (1993) respectively.

We report the discovery of non-radial pulsations with at least 4 periods in the B7V star HD 37151. This result is based on 465 photometric measurements spanning 12 years. In addition, 30 high-resolution spectra were taken in the Mgii λ4481 region: they show a small projected rotational velocity and slight variations of the line profiles. Although this star was once classified B8Vp(Si), all available data show it is a normal B7V star. It is the second coolest SPB star found to date.

ET And is a binary system with a B9 Si star as the main component (Porb = 48.308d, e=0.46). Controversial claims in the literature concerning pulsation with periods ranging from few minutes to few hours and with variable amplitudes indicated a challenging target and motivated us to organize several photometric and spectroscopic observing campaigns. The problem with pulsation of ET And is that Teff and log g put this star in the cool domain of Slowly Pulsating B-type (SPB) stars, but the pulsation periods would be too short by a factor of about four, relatively to the shortest hitherto known periods for SPB stars.

δ Scuti are pulsating stars with a characteristic period of several hours, lying in the A2-F5 spectral range and placed on or a little above the main sequence. Unlike the well-known “classical” RR Lyrae or Cepheids, which show a homogeneous pulsational behaviour (i.e. radial modes with large amplitudes), δ Scuti stars have peculiarities: their amplitudes vary from millimagnitudes to tenths of magnitude and their pulsation modes can be both radial and non-radial.

At the 1992 GONG Meeting in Boulder (ASP Conf. Ser. Vol. 42) an attempt was done to form a group of people interested in multiobject, multisite observations with CCD cameras on moderate size telescopes (D ≈ 1m). The motivations is the need for uninterrupted, long time strings of photometry of certain types of variables. Observations of single objects by networks of photoelectric photometers have been practiced for some time. The extension to multiobject, differential CCD photometry not only multiplies the output, but also provide better signal/noise results. Many of the objects of interest (δ-Scuti's, β-Cephei's) are found close together in open clusters, which already serve as testbeds for stellar evolution theories. Nevertheless, suitable target fields are difficult to find.